Hey David. This is an interesting issue; I’m seeing it myself on your site, too. However when I attempt to recreate on my default 2011 install it works fine and I can access the category-specific pages without issue. This makes me think something else might be at play here.
Have you already flushed your permalinks (just resaving the permalinks page, without making any changes)? That might do the trick here, but if not we should check for a conflict with another plugin or the theme. This would involve deactivating other plugins until just The Events Calendar/PRO + the theme are on; and if the issue persists, reverting to the default 2011 theme from there. It’d be awesome if you had a test environment on which to do this.
Lastly: I don’t know how much impact this would have, but can you try testing without the ‘home’ in the URL there?